A Riemann-Stein Kernel Method
Statistics Theory
2022-01-12 v4 Statistics Theory
Abstract
This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior distributions supported on a compact Riemannian manifold, and we relate these to a kernel Stein discrepancy (KSD). Moreover, we prove in our setting that the KSD is equivalent to Sobolev discrepancy and, in doing so, we completely characterise the convergence-determining properties of KSD. Our contribution is rooted in a novel combination of Stein's method, the theory of reproducing kernels, and existence and regularity results for partial differential equations on a Riemannian manifold.
Cite
@article{arxiv.1810.04946,
title = {A Riemann-Stein Kernel Method},
author = {Alessandro Barp and Chris. J. Oates and Emilio Porcu and Mark Girolami},
journal= {arXiv preprint arXiv:1810.04946},
year = {2022}
}